Do we have an idea of what they would look like to the naked human eye?
I.e. You would be able to see the front and the back of the star simultaneously. It looks like a weird morphing Mercator projected map.
Here is a random video showing the idea, I have no idea how precise the simulation is though.
https://www.reddit.com/r/spaceengine/comments/15d3xwd/how_co...
As it happens, the sun is such an object. And it more or less makes sense that we have eyes tuned to pick up the dominant wavelength arriving from our local light source.
Edit: the wikipedia page has a great animated chart of this effect, showing what the visible-only spectrum looks like as temperature changes: https://en.wikipedia.org/wiki/Color_temperature
Far in the future once neutron stars have cooled, what would they look like? If you shone light on it, would it absorb it? Reflect it? Etc
It's not certain what their surface would be like, physics just isn't developed enough to provide a definite answer.
The trivial case of an isolated cold neutron star is: completely black, other than a very slight far infrared glow of whatever their remaining thermal radiation is.
An educated guess is that an externally illuminated cold neutron star would look extremely smooth and "dark grey". Most current models propose that young and hot neutron stars have an atmosphere of metal plasma. Presumably this would freeze out into a thin surface layer as the stars cool.
A complication is that their surface gravity is so high that inbound "white" light would be shifted well into the UV range, which would interact with the surface very differently to visible light. Reflected light would be redshifted back out to the original white, but any light that's absorbed and re-emitted would likely take on interesting colours.
Here's a chart of metal surface reflectivity by wavelength: https://www.researchgate.net/figure/Spectral-reflectivity-of...
As you can see, most metals don't reflect much in the UV range, but there are peaks and troughs.
Depending on the exact surface composition, you might see different colours than what you'd normally expect for metals.
You'd also have to take the rotation rate into account. If there's any inconsistency in the surface albedo, you'd see "horizontal stripes" for fast-spinning stars, or flickering for slower spinning ones.
How could any atmosphere exist in gravity that strong?
Dragon’s Egg is a great sci-fi book that explores what life on such a world might be like.
Normal matter is like expected personal space in Finland. Everyone maintains a respectful distance, and they like it that way. Sometimes no one sees another human up close for days, let alone actually does anything resembling ‘touch’.
Neutron stars are like a giant coked up swinger orgy pile. Sometimes you can’t even tell where one person begins, and the next one ends, and certainly no one cares much anyway.
The surface of a neutron star is covered with a thin shell of protons and electrons in essentially random configurations, so it would absorb and emit light in all sort of random frequencies.